Question from Monday (3/2/15): Can the 1-degree mantle

convection that may have formed the crustal dichotomy also explain

the Southern hemisphere magnetic stripes?

Keller and Tackley, 2009, Towards self-consistent modeling of the martian dichotomy: The influence of one-ridge convection on crustal thickness

distribution, Icarus 202, 429-443.

• The dominant feature of the crustal thickness distribution obtained from one-ridge convection in the mantle is a characteristic, roughly elliptical shape that shows a striking first- order similarity to the shape of the martian dichotomy.

• The most important process leading to the formation of this shape is massive decompression melting and time-dependent behavior of the ridge-like upwelling, which in itself can be seen as a link between two superplumes at each end.

• This configuration allows for the formation of massively thick crust spread over an area comparable to the martian highlands.

• Furthermore, our results suggest that northern lowland basement crust was formed either shortly before or simultaneously with the southern highlands.

• The linear patterns of magnetic reversals discovered on large parts of the southern and some parts of the northern hemisphere (Connerney et al., 1999) could be related to subsequent stages of time-dependent one-ridge convection, as the geometry of these features coincide with our interpretation of how a one-ridge convective pattern would have been positioned in the mantle to form the dichotomy.

Crustal thickness for models with increasing Rayleigh number

What is Rayleigh number?

• In fluid mechanics, the Rayleigh number (Ra) for a fluid is a dimensionless number associated with buoyancy driven flow (also known as free convection or natural convection). When the Rayleigh number is below the critical value for that fluid, heat transfer is primarily in the form of conduction; when it exceeds the critical value, heat transfer is primarily in the form of convection.

• For free convection near a vertical wall, the Rayleigh number is defined as

• where• x = Characteristic length (in this case, the distance from the leading edge)• Rax = Rayleigh number at position x

• Grx = Grashof number at position x• Pr = Prandtl number• g = acceleration due to gravity• Ts = Surface temperature (temperature of the wall)

• T∞ = Quiescent temperature (fluid temperature far from the surface of the object)• ν = Kinematic viscosity• α = Thermal diffusivity• β = Thermal expansion coefficient (equals to 1/T, for ideal gases, where T is absolute

temperature)

Occam’s RazorAmong competing hypotheses that predict equally well, the one with the fewest assumptions should be selected. Other, more complicated solutions may ultimately prove to provide better predictions, but—in the absence of differences in predictive ability—the fewer assumptions that are made, the better.